Laguerre-type special functions and population dynamics

We introduce new Laguerre-type population dynamics models. These models arise quite naturally by substituting in classical models the ordinary derivatives with the Laguerre derivatives and therefore by using the so called Laguerre-type exponentials instead of the ordinary exponential. The L-exponentials e(n)(t) are increasing convex functions for t >= 0, but increasing slower with respect to exp t. For this reason these functions are useful in order to approximate different behaviors of population growth. We consider mainly the Laguerre-type derivative D(t)tD(t), connected with the L-exponential el(t), and investigate the corresponding modified logistic, Bernoulli and Gompertz models. Invariance of the Volterra-Lotka model is mentioned. (C) 2006 Elsevier Inc. All rights reserved.